📚 Topic Summary
Vector operations, when performed algebraically, involve manipulating vectors using their components. This allows us to perform addition, subtraction, and scalar multiplication in a precise and straightforward manner. Understanding these operations is fundamental for further studies in physics and engineering.
Think of a vector as an arrow with a specific length and direction. Algebraically, we represent it as a set of numbers (components). To add vectors, we simply add their corresponding components. Scalar multiplication involves multiplying each component of a vector by a scalar (a single number).
🧠 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Scalar |
a. A quantity with both magnitude and direction |
| 2. Vector |
b. The result of adding two or more vectors |
| 3. Component |
c. A quantity with only magnitude |
| 4. Resultant Vector |
d. Multiplying a vector by a scalar |
| 5. Scalar Multiplication |
e. The horizontal or vertical value of a vector |
✏️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
A ______ is a quantity with both magnitude and direction. When adding vectors algebraically, we add their corresponding ______. A ______ is a quantity with only magnitude and multiplying it by a vector is called ______ resulting in a new vector. The ______ is the vector obtained when adding two or more vectors together.
🤔 Part C: Critical Thinking
Explain in your own words how algebraic vector operations make solving physics problems easier. Provide a specific example.